"I didn't pay attention to the game," Cano said. "You don't want that to happen. There was nothing I could do after that. … I'm human. I make mistakes. But those are the kind of things I shouldn't let happen again."
Cano tried scampering back to third after Rodriguez threw the ball home, but he was retired when catcher Yasmani Grandal threw to third baseman Juan Uribe in what officially was scored as a caught stealing.
The out was the second of the inning and Seattle's rally quickly died when Mike Zunino grounded out for the third out.
Cano acknowledged it was probably the worst mistake he's made in a game.
"I would say yes. I felt in that situation the dumbest guy in the game," he said. "I wish he'd thrown it into left field. Those are the things that make you embarrassed, being in the game so long and those little things happen in a game. I told the manager, 'It's my fault, I should have been paying attention.'"
The Mariners did have the bases loaded after Austin Jackson reached on an error, Cano singled and Nelson Cruz walked. Kyle Seager followed with a groundout to first that scored Jackson from third to cut Seattle's deficit to 5-2. That play moved Cano and Cruz up a base, setting up the second-and-third situation for Morrison.
The Dodgers swept the Mariners in the three-game series as Seattle -- a club expected to challenge for the AL West title -- is off to a 3-6 start. Cano said lessons can be learned now that will help down the road.
"You have to give credit to [the Dodgers]," he said. "They did a good job with men in scoring position and came back and beat us twice. Those are little things that maybe we need to remember later down the road.
"That's a little message. You have to play nine innings. Don't live on your expectations. I know people were saying we're the team to play to go to the World Series. But we have to play now. You have to win now. We can't worry about later. We've got to put things together."
Greg Johns is a reporter for MLB.com. Follow him on Twitter @GregJohnsMLB as well as his Mariners Musings blog. This story was not subject to the approval of Major League Baseball or its clubs.